Timing meals before running

I need advice.  When do you run in relation to what you've eaten?  And what have you eaten?

 I've been running in the morning,  However, I can't abide solids first thing in the day, so I have a protein coffee (made with 1 1/2 scoops powder) about an hour before I set out on my run.  That usually makes it 9:30 or 10:00 before I'm off.  Now that it's getting warmer, and I'm anticipating going back to work sometime soon, I want to push off first thing in the morning, like at 5:00 a.m. before I've eaten or at most had a sip of water.  Is that a good idea?  I'm only going 2-3 miles on these runs.